Yes you can build your own lower.
No serial # is needed unless you want to sell it, and at the time of sale it would need a serial #.
Now, PA13-3 would have to be examined in respect to the lower built.
If you have all the parts needed to produce an "assault weapon" except for the lower, then producing the lower may create a circumstance where you produced an assault weapon and created it past the point of the time in which you could have had one.
Now if you build a lower but do not have all the parts required by the law to be able to rapidly assemble it into an assault weapon (what is meant by rapidly????)
Now looking at the characteristics that make an assault weapon (because your home made gun would not be one specifically listed or by a manufacture of any listed) one can examine the gun parts needed from PA13-3:
[(ii) A] (II) Any grip of the weapon, including a pistol grip, [that
protrudes conspicuously beneath the action of the weapon;] a
thumbhole stock, or any other stock, the use of which would allow an
individual to grip the weapon, resulting in any finger on the trigger
hand in addition to the trigger finger being directly below any portion
of the action of the weapon when firing; or
The above section would likely cover your "AR15" ... and following this...definition of action comes into play..which is:
(3) "Action of the weapon" means the part of the firearm that loads,
fires and ejects a cartridge, which part includes, but is not limited to,
the upper and lower receiver, charging handle, forward assist,
magazine release and shell deflector;
So if you have the parts listed above (and a pistol grip which I would assume, being a "AR style" .. all the parts listed...then your manufacture of a finished lower would especially create a new AR at the time that the lower is produced.
Of course, one would have needed to have all the parts on/before 5 APR 13 to be legal.
Now, if you do not have all the parts required to be mandatory for an "assault weapon", you can finish 1000 lowers w/o it being in violation of the law.
If you want to speak further on the matter...PM me.
Right now, today .. if you have the parts to complete an AR but the lower and you finish a 80% lower into a 100% lower ~ you may run into felony charges.